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{"title":"Dynamical Behavior and Expressions of Solutions of a Class of Higher-Order Nonlinear Difference Equations","authors":"Ghada AlNemer, Lama Sh. Aljoufi, A. M. Ahmed, Samir Al Mohammady, M. Zakarya, H. M. Rezk","doi":"10.1155/2024/7104474","DOIUrl":null,"url":null,"abstract":"The aim of this article is to get the forms of the solutions of the following nonlinear higher-order difference equations <span><svg height=\"16.2017pt\" style=\"vertical-align:-3.943501pt\" version=\"1.1\" viewbox=\"-0.0498162 -12.2582 32.251 16.2017\" width=\"32.251pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.981,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.448,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,16.008,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,24.62,0)\"></path></g></svg><span></span><svg height=\"16.2017pt\" style=\"vertical-align:-3.943501pt\" version=\"1.1\" viewbox=\"35.8331838 -12.2582 45.521 16.2017\" width=\"45.521pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g 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xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,249.646,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span></span> where the initial conditions <span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 19.952 14.8173\" width=\"19.952pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-244\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,6.981,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.541,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,16.988,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"22.0811838 -9.28833 16.763 14.8173\" width=\"16.763pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g 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xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"65.2421838 -9.28833 9.204 14.8173\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,65.292,0)\"><use xlink:href=\"#g113-51\"></use></g><g transform=\"matrix(.013,0,0,-0.013,71.532,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"76.6251838 -9.28833 18.427 14.8173\" width=\"18.427pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,76.675,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,81.818,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,86.961,0)\"><use xlink:href=\"#g113-47\"></use></g><g 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height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"47.8941838 -9.28833 18.047 11.5564\" width=\"18.047pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,47.944,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,53.087,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,58.23,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,61.228,0)\"></path></g></svg></span> are arbitrary real numbers. Also, we examine stability, boundedness, oscillation, and the periodic nature of these solutions.","PeriodicalId":55177,"journal":{"name":"Discrete Dynamics in Nature and Society","volume":"228 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Dynamics in Nature and Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/7104474","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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